Question

How to Rationalize the denominator of 6-4√2/6+4√2

Answer 1

Answer:

17 - 3√2

Step-by-step explanation:

Given that ;

$\sf \dfrac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} }$

To rationalise the denominator, multiply the numerator and denominator by the rationalising factor, i.e., (6 - 4 √2).

$\sf \frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } \\ \\ \sf \frac{6 - 4 \sqrt{2} }{6 + 4 \sqrt{2} } \times \frac{6 - 4 \sqrt{2} }{6 - 4 \sqrt{2} } \\ \\ \sf \frac{(6 - 4 \sqrt{2}) {}^{2} }{(6) {}^{2} - (4 \sqrt{2} ) {}^{2} } \\ \\ \sf \frac{(6) {}^{2} + (4 \sqrt{2})^{2} - 2 \times 6 \times 4 \sqrt{2} }{36 - 32} \\ \\ \sf \frac{36 + 32 - 12 \sqrt{2} }{4} \\ \\ \sf \frac{4(9 + 8 - 3 \sqrt{2}) }{4} \\ \\ \implies \sf 17 - 3 \sqrt{2}$

Hence, the answer is (17 - 3 √2).